Charged black hole and radiating solutions in entangled relativity

TL;DR

This paper investigates black hole solutions in entangled relativity, showing that the external Schwarzschild metric approximates these solutions well, especially for charged and radiating black holes, and discusses potential extensions to rotating cases.

Contribution

It demonstrates that the Schwarzschild metric effectively models black holes in entangled relativity and explores solutions involving electromagnetic fields and radiation.

Findings

Schwarzschild metric approximates black holes in entangled relativity

Charged black hole solutions align with dilaton theory results

Radiating solutions in entangled relativity agree with general relativity

Abstract

In this manuscript, we show that the external Schwarzschild metric can be a good approximation of exact black hole solutions of entangled relativity. Since entangled relativity cannot be defined from vacuum, the demonstrations need to rely on the definition of matter fields. The electromagnetic field being the easiest (and perhaps the only) existing matter field with infinite range to consider, we study the case of a charged black hole -- for which the solution of entangled relativity and a dilaton theory agree -- as well as the case of a pure radiation -- for which the solution of entangled relativity and general relativity seem to agree, despite an apparent ambiguity in the field equations. Based on these results, we argue that the external Schwarzschild metric is an appropriate mathematical idealization of a spherical black hole in entangled relativity. The extension to rotating cases is briefly discussed.